To fully realise the combined potential of next generation aircraft and engine technologies an integrated multiphysics design approach is essential. In this context the German Aerospace Center (DLR), the French Aerospace Lab (ONERA) and Airbus are currently developing CODA (CFD ONERA DLR \Airbus), a next-generation CFD solver for aircraft and turbomachinery design, devised to be able to fully exploit current and future HPC architectures~\cite{Goertz2022}. Beyond robust and efficient numerical discretization schemes, the efficient and accurate simulation of modern propulsion systems requires a number of specific numerical boundary conditions. In the context of time-accurate simulations, one such essential boundary condition is that which is used to couple adjacent domains (i.e. blade rows) in a time-accurate and conservative manner. The focus of this paper is therefore the implementation and analysis of a domain-coupling algorithm in CODA that is tailored to the physics of blade-row-interactions. The approach implemented is based on a temporal and spatial Fourier decomposition of the flow field along the interface boundaries and allows, when combined with phase-shifted periodic boundary conditions, the simulation of stages with arbitrary blade-count ratios using only a single passage per blade row. A challenge that arises due to the use of temporal Fourier data in conventional time-domain simulations is that these data are not immediately available, but rather must be computed iteratively from the available instantaneous flow data. To mitigate potential stability issues that this may cause we therefore investigate in detail the impact of the formulation of the boundary condition using characteristic variables and compare the results with alternative approaches. To verify the approach a number of test cases are presented, ranging from the advection of a harmonic entropy wave in a simple duct to the URANS simulation of a fan-stage.